Chapter 4.3, Problem 4BCYP

To determine

The equation of line ST for the graph shown below in standard form.

  

Answer to Problem 4BCYP

The equation of line is $x+y=12$ .

Explanation of Solution

Given:

The given quadrilateral RSTU has vertices $R\left(1,5\right),S\left(4,8\right),T\left(7,5\right)\text{ and }U\left(4,2\right)$ .

Calculation:

The slope $\left(m_{ST}\right)$ for the line ST through the points $S\left(4,8\right)\text{ and}T\left(7,5\right)$ using slope formula is evaluated as,

  $\begin{array}{c}\left(m_{ST}\right)=\frac{5-8}{7-4}\\ =-1\end{array}$

Now, the equation for line ST having slope $\left(m_{ST}=-1\right)$ and passing through the point $S\left(4,8\right)$ is evaluated as,

  $\begin{array}{c}y-y_1=m_{ST}\left(x-x_1\right)\mathrm{......}\left(\text{Point-slope form}\right)\\ y-8=-1\left(x-4\right)\mathrm{......}\left(\begin{array}{l}\text{Here }{m}_{ST}=-1\\ \left(x_1,y_1\right)\to \left(4,8\right)\end{array}\right)\\ y-8=-x+4\\ \text{or, }x+y=\mathrm{12......}\left(\text{Standard form}\right)\end{array}$